For chocolate chip cookie layers, preheat oven to 325 °F and grease 2 9-inch cake pans, lining the bottoms with parchment paper.
Cream butter, both sugars and corn syrup until smooth. Add eggs and vanilla extract and combine well. In a separate bowl, stir flour with cornstarch, baking soda and salt to blend. Add flour to butter mixture and stir until dough just comes together. Stir in chocolate chips. Divide dough evenly between the two cake pans and spread to level the dough. Bake for 20 to 25 minutes, until cookie turns a light golden brown. Allow to cool completely.
For chocolate chip ice cream, whisk egg yolks, sugar and cornstarch in a saucepot to combine. Whisk in half & half cream and stir mixture over medium-low heat until it thickens and become just a little glossy, about 8 minutes. Remove from heat and strain. Stir in vanilla and let mixture cool to room temperature, stirring occasionally, then chill completely. Whip cream to soft peaks and whisk into chilled ice cream. Pour mixture into an ice cream maker following manufacturer’s instructions. Just before removing ice cream, pour in chocolate chips. Scrape ice cream into a container and freeze while preparing cookies for assembly (if ice cream is still quite fluid, freeze for about 40 minutes to firm up – this will prevent chocolate chips from sinking).
For assembly, turn cookies out of pan and peel off parchment. Line the side of a 9-inch springform pan with plastic wrap and place one cookie layer, nice side down into lined pan. Remove ice cream from freezer and spread over cookie. Lay remaining cookie layer on top of ice cream, pressing only lightly. Wrap cake and freeze until ready to serve.
To serve, let cake temper (soften) at room temperature for at least 15 minutes. Remove springform pan and peel away plastic wrap. Slice into wedges and serve.